Immiscible Displacement in Porous Media: Stability Analysis of Three-Dimensional, Axisymmetric Disturbances With Application to Gravity-Driven Wetting Front Instability

Existing continuum models of multiphase flow in porous media are unable to explain why preferential flow (fingering) occurs during infiltration into homogeneous, dry soil. We identify a relevant pattern-forming mechanism in the dynamics of the wetting front, and present a macroscopic model that reproduces the experimentally observed features of fingered flows. The proposed model reveals a scaling between local and nonlocal interface phenomena in imbibition, and does not introduce new independent parameters. The predictions based on this model are consistent with experiments and theories of scaling in porous media.

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Wetting front instability: 2. Experimental determination of relationships between system parameters and two-dimensional unstable flow field behavior in initially dry porous media

Water Resources Research ◽

10.1029/wr025i006p01195 ◽

1989 ◽

Vol 25 (6) ◽

pp. 1195-1207 ◽

Cited By ~ 156

Author(s):

R. J. Glass ◽

T. S. Steenhuis ◽

J-Y. Parlange

Keyword(s):

Porous Media ◽

Flow Field ◽

Experimental Determination ◽

Two Dimensional ◽

Wetting Front ◽

Unstable Flow ◽

System Parameters ◽

Front Instability ◽

Field Behavior

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Immiscible Displacement at Pore Level for Correlated Porous Media

International Journal of Modern Physics C ◽

10.1142/s0129183198000777 ◽

1998 ◽

Vol 09 (06) ◽

pp. 837-849 ◽

Cited By ~ 1

Author(s):

A. M. Vidales ◽

J. L. Riccardo ◽

G. Zgrablich

Keyword(s):

Porous Media ◽

Pore Space ◽

Three Dimensional ◽

Immiscible Displacement ◽

Porous Network ◽

Buoyancy Forces ◽

Correlation Strength ◽

Pore Level

Immiscible displacement at pore level on a three-dimensional correlated porous network is simulated allowing flow of the wetting phase along crevices of the pore walls (possibility of snap-off in throats) and advance through the centers of the pore space with different pore and throat filling conditions, leading to a cooperative filling. When these two mechanisms compete, different patterns arise. We study the effect of the correlation strength on the onset of each pattern. We do not take buoyancy forces into account.

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The Onset of Instability During Two-Phase Immiscible Displacement in Porous Media

Society of Petroleum Engineers Journal ◽

10.2118/8371-pa ◽

1981 ◽

Vol 21 (02) ◽

pp. 249-258 ◽

Cited By ~ 109

Author(s):

Ekwere J. Peters ◽

Donald L. Flock

Keyword(s):

Porous Media ◽

Stability Analysis ◽

Stability Theory ◽

Critical Value ◽

Immiscible Displacement ◽

Dimensionless Number ◽

Two Phase ◽

Displacement Front ◽

The Stability ◽

Scaling Group

Abstract This paper presents a dimensionless number and its critical value for predicting the onset of instability during immiscible displacement in porous media. The critical dimensionless number obtained from a stability theory for a cylindrical system successfully predicted the onset of instability in laboratory floods. Therefore, this number can be used to classify the stability of two-phase incompressible displacements in homogeneous porous media. Introduction When a fluid displaces a more viscous fluid, the displacement front may become unstable, resulting in viscous fingering. This phenomenon raises both practical and theoretical concerns. Apart from further reducing the displacement efficiency of an already inefficient displacement arrangement, instability may invalidate the usual method of simulating immiscible displacement performance based on relative permeability and capillary pressure concepts. Also, it introduces an additional scaling requirement for using model tests to forecast prototype displacement results. Therefore, it would be most beneficial to predict the onset of instability, so as to avoid viscous fingering, or, where it is unavoidable, to be able to recognize it as a factor in the displacement.The onset of instability call be predicted by a stability analysis of the displacement. The objective of such an analysis is to determine the conditions under which small disturbances or perturbations of the displacement front will grow to become viscous fingers. Ideally, the analysis should give a universal dimensionless scaling group together with its critical value above which instability will occur. The stability classification then would entail no more than the calculation of one dimensionless number in a manner analogous to the calculation of a Reynolds number to distinguish between laminar and turbulent flow.Several stability studies of immiscible displacement have been reported in the literature. Collectively, they show that these variables are pertinent to the stability problem:mobility (or viscosity) ratio,displacement velocity, system geometry and dimensions,capillary and gravitational forces, andsystem permeability and wettability. However, none of the previous studies have combined these variables into one dimensionless number that can be used to quantify the stability classification.The objective of this study was to obtain, by means of a stability analysis, a universal dimensionless scaling group and its critical value for predicting the onset of instability during immiscible displacement in porous media. This paper shows how the stability theory of Chuoke et al. was extended to achieve this objective and presents the results of laboratory floods that confirm the predicted onset of instability in cylindrical cores. Theory The pertinent dimensionless number for predicting the onset of instability was obtained by extending the stability theory of Chuoke et al. Their theory was based on a piston-like unperturbed displacement model in which the oil and water zones are separated by a planar interface. Details of the theory and our extension of it are presented in the following sections. SPEJ P. 249^

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Experimental Studies of Wetting Front Instability Induced by Gradual Change of Pressure Gradient and by Heterogeneous Porous Media

Soil Science Society of America Journal ◽

10.2136/sssaj1977.03615995004100030010x ◽

1977 ◽

Vol 41 (3) ◽

pp. 483-489 ◽

Cited By ~ 48

Author(s):

I. White ◽

P. M. Colombera ◽

J. R. Philip

Keyword(s):

Porous Media ◽

Pressure Gradient ◽

Experimental Studies ◽

Heterogeneous Porous Media ◽

Gradual Change ◽

Wetting Front ◽

Front Instability

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A Characteristic Finite Difference Domain Decomposition Substructuring Method for Immiscible Displacement Problems in Three-Dimensional Porous Media

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.629.915 ◽

2012 ◽

Vol 629 ◽

pp. 915-919

Author(s):

Chang Feng Li

Keyword(s):

Porous Media ◽

Finite Difference ◽

Domain Decomposition ◽

Domain Decomposition Method ◽

Three Dimensional ◽

Accurate Solution ◽

Immiscible Displacement ◽

Two Phase ◽

Fully Implicit ◽

Discrete Norm

Two-phase immiscible displacement in porous media is described by a coupled nonlinear system of an elliptic equation (for the pressure) and a parabolic equation (for the saturation). For the saturation changes much rapidly than the pressure, a more accurate solution (in both time and space) should be illustrated in practical numerica simulaiton for the former unknown. In this paper we present a seven-point central finite difference scheme to simulate the pressure and a characteristic finite difference combinng with domain decomposition method for the saturation equation. This method consists of reduced two-dimensional computation on the subdomain interface boundaries and fully implicit computation parallelly in subdomains. Aparallel algorithm is outlined and an error estimate in discrete norm is derived by introducing new inner products and norms. At the end of this paper, numerical experiments are presented in order to demonstrate theoretical results and the efficiency.

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